Is it allowed to distribute my game on my own web-site after I have sent it to the 4e4 contest and accepted legal agreements? Moreover, I would like to know, whether I can use my models of the entry to the 4e4 contest in other games which I might produce in the future? Thank you for your help in advance.

Quote: Legal section Four Elements IV Contest page
The entrant retains any and all rights of ownership, intellectual property rights and all other rights entrant may have in and to the entry

So yes, you are the owner of the entry and therefor free to put it on a webpage, sell it or use parts of it in other games.